Research

Research interest: My primary interest lies in Analysis and Partial differential equations. More precisely, I am broadly interested in the Calculus of Variation and Analysis of PDE models related to Fluid Mechanics and Celestial Mechanics. In addition, I hold an implicit and lukewarm interest in Optimization and Machine learning. 

Preprint

#1 Exponential Lower Bounds for the Advection-Diffusion Equation with Shear Flows Yupei Huang and Xiaoqian Xu.  arXiv preprint:   arXiv:2511.14512 

Publication

#1 Formation of singularity for the classical solutions of the rotating shallow water system. Yupei Huang and Chunjing Xie. Journal of Differential Equations 348 (2023): 45-65.

#2 Regular and Singular Steady States of 2D incompressible Euler equations near the Bahouri-Chemin Patch. Tarek, Elgindi and Yupei Huang. Archive for Rational Mechanics and Analysis 249 (1), 1-31

#3 On the rigidity of uniformly rotating vortex patch near the Rankine vortex   Yupei Huang. Nonlinearity(2025)

#4 H{ö}lder convergence of singular steady states to Bahouri-Chemin patch  Yupei Huang and Chilin Zhang.  Calculus of Variations and Partial Differential Equations 64 (6), 1-31

#5 A Classification Theorem for Steady Euler Flows Tarek M. Elgindi, Yupei Huang, Ayman R. Said and Chunjing Xie. To appear in Duke Mathematical Journal